Splitting Sections off an Object
I'm not sure if you're asking how to assign multiple Materials to the same Mesh or how to split one Object into two.

If you just want to Split a Mesh into two, the easiest way is to select all faces you need, hit "P" and then click "By Selection".

To create a 2. Material go to the Materials Tab and hit the "+" icon. Select all  the faces you want to share this Material and then hit "Assign" in the Materials Tab.